Tuesday, April 03, 2012

A monetary policy Pascal's Wager

In the 1600s, French philosopher-mathematician Blaise Pascal made the following argument for believing in God: "If I believe in God, and I'm right, I'll go to Heaven, which is infinitely awesome. But if I don't believe in God, and I'm wrong, I'll go to Hell, which is infinitely bad. Therefore, it makes sense to believe in God." Any economist will recognize this as being an expected utility calculation - even if there is only a tiny chance that God is real, the expected utility of believing in God is still infinitely higher than the expected utility of not believing in God. So believe in God, ye rational agents!

The problem is, as you probably figured out before you even finished reading that paragraph, is that it assumes that you only have two choices - Christianity and atheism. Suppose we also introduce Islam. Suppose the Christians say "If you believe in Jesus you'll go to Heaven; if not, Hell." And suppose the Muslims say "If you believe in Allah you'll go to Heaven; if not, Hell." Call this the Two-Sided Pascal's Wager. Well, in this case, your expected utility is undefined no matter which religion you choose. And you can't choose both! You are basically screwed. Maybe you end up choosing one or the other, but you always reserve the right to switch.

This is interesting, because it means that Taylor believes that the Fed's decisions have absolutely enormous power over the macroeconomy. I know Suppose, hypothetically, that I know someone else who believes the same thing: Scott Sumner just for fun let's call him "Scott Sumner" (Update: This does not seem to characterize Scott Sumner's actual position. See bottom of post. For now, go with the hypothetical.). Also, Suppose both Taylor and Sumner appear to believe that Fed commitment to an optimal monetary policy rule is essential to prevent large recessions. And each economist has a very specific idea of what that optimal rule should be.

Here's the weird thing, though: Their rules are different rules.

Taylor basically says: "If the Fed does not credibly commit to a Taylor rule with coefficients of 1.5 and 0.5, the economy will experience big recessions and/or big inflations."

So suppose you are a central banker, and you are very very risk-averse. You absolutely dread big recessions and big inflations. If you pick the wrong monetary policy rule, you're absolutely screwed. But you also have model uncertainty; you don't know for sure whether Taylor's story or Sumner's story perfectly describes the world.

Well, since you're risk-averse, you'd ideally like to choose a mix of the two rules. You'd like to buy insurance. But you can't buy insurance, because there is no way to mix the two rules! Both Taylor's and Sumner's models each insist that for the policy to work, there can be no wavering from firm commitment to the rule. Your choice set is convex.

In this case, Taylor's and Sumner's dueling propositions look very much like a Two-Sided Pascal's Wager between Christianity and Islam. You are a risk averse agent faced with a convex choice set over two high-risk alternatives, with no low-risk alternative available. In other words, you are screwed.

This is why I think that economists who advocate models in which A) small monetary policy mistakes have severe negative consequences, and B) commitment is crucial are, ironically, doomed to failure by the extreme nature of their own arguments. The central bank operates under a great deal of model uncertainty, and is highly risk-averse. Unless it is extremely confident of one single model of the macroeconomy, the Fed will choose discretion (or a model like Woodford's, in which deviating from the rule does not come at a huge cost) rather than the kind of rigid commitment advocated by economists like Taylor. Which is to say, even if the Fed picks a rule, it will reserve the right to modify or drop that rule if conditions seem to warrant, just like a person reserves the right to change their religion. And since people know that the Fed reserves that right, they will never believe that the Fed will ever fully commit to any rule. Which means that no rule that requires absolute commitment can work.

This leaves discretion as the only feasible policy. The Two-Sided Pascal's Wager is a wager you just can't win.

Update: Commenters, including Scott Sumner, have suggested that the position I initially attributed to Sumner is more characteristc of economists other than Sumner. If so, I apologize for mischaracterizing Sumner's opinion, but really I was just trying to use any example in order to demonstrate the general principle.

Update 2: In a Twitter discussion, Andy Harless raises the possibility that Fed commitment to any rule might dominate pure discretion. Scott Sumner (I think) puts forth the same idea in the comments. Fair enough. That could be true! But, given that John Taylor disagrees - that he thinks that any non-Taylor rule will spell disaster - and given that the Fed gives Taylor's ideas nontrivial levels of credence, my point still holds!

Update 3: In the aforementioned Twitter discussion, I said:

My point is that if the Fed gives Taylor ANY credence, no one else will persuade the Fed to commit firmly to a non-Taylor rule...Let me put my point more informally: Taylor probably scares the Fed away from credibly committing to ANY non-Taylor rule...just by invoking Hell, Taylor is FORCING a Pascal's Wager on the Fed, regardless of what [any other economist] does or who is right.

That should clear things up, for those who found the above discussion a bit dense.

Clever, but I strongly disagree. I do not claim it's my way or the highway. Nor do I believe that small monetary policy errors cause big recessions. I believe that huge monetary errors cause big recessions. I believe that any plausible monetary policy (mine, Taylor's, Woodford's, etc) would have prevented the Great Recession, at least as long as policy was forward-looking (and Bernanke claims it is.) I just happen to think mine would have done so best.

I think Taylor's argument would be that his rule is robust to a number of models: his 1993 paper emphasized that it worked very well in several of the large scale macro models with which he was involved at the time. It also works well is small scale NK models a la Woodford (2003). I suspect the NGDP rule would also work well in the same kind of models. Both Sumner and Taylor would probably agree that using either rule is better than making policy under discretion, and this result will again apply to a very wide range of models.

Excellent observation, although I am not sure anyone is advocating that small deviations result in big consequences.

maybe the Taylor and Sumner example was not the best because Taylor rules are (mostly) a special case of an NGDP rule (see the recent dallas Fed paper). If you look at NK models they also have an CB "utility" or objective which implies a Taylor-type (or NGDP rule under certain conditions, like wage stickiness). Also Taylor and Sumner would I think disagree on whether the Fed should steer with the monetary base or interest rates.

{Both rules are "robust to a number of models" the issue is that the degree of wage stickiness for example is unknown and may even vary}.

I do not think the policy error was "small." The Fed went out and tried to prick the "housing bubble." Home ownership rate in U.S. is 65%, and the S&L crisis was well know and expensive. If you mess with a bear, it mauls you, unless you have a backup plan.

Scott you said, "Clever, but I strongly disagree. I do not claim it's my way or the highway. Nor do I believe that small monetary policy errors cause big recessions. I believe that huge monetary errors cause big recessions. I believe that any plausible monetary policy (mine, Taylor's, Woodford's, etc) would have prevented the Great Recession, at least as long as policy was forward-looking (and Bernanke claims it is.) I just happen to think mine would have done so best."

Well at least you admit it's clever. Finally get to talk to you outside of class-LOL. I certainly thought so. However, Woodford's rule is basically one that is not rigid-"deviating from the rule does not come at a huge cost."

I did a post that looked at Taylor and company-one in the company of course being Scott. http://diaryofarepublicanhater.blogspot.com/2012/04/sumner-and-glasner-on-beckworth-on.html

I see Scott Sumner already commented. I was going to say I think the post characterizes his position unfairly, but he beat me to it. I think, however, you make a reasonably fair characterization of Taylor's position. I think it would also be a reasonably fair characterization of Beckworth's position, since he makes the same "The Fed was too easy in 2003-2005 because it didn't follow my rule" argument as Taylor does. Since Beckworth's rule differs from Taylor's, you could make your same argument using Taylor vs. Beckworth rather than Taylor vs. Sumner.

But it still isn't an unconditional argument for discretion over rules. It's just an argument that people who are very picky about the exact rule are undercutting their own argument for having rules in the first place. I do think that, when Taylor and Beckworth criticize the 2003-2005 Fed, they are tending to weaken, not strengthen, their case for rule-based monetary policy. But since I don't find their criticisms at all cogent, I don't think they really weaken the case for rules over discretion. They just mean that a few particular rule advocates haven't really thought things through.

Here's the point: Suppose there exists a model A in which deviations from a certain rule have big negative consequences. Suppose that the Fed assigns a nontrivial probability to A being true. Now suppose there exists a model B which requires firm and rigid commitment from the Fed in order to produce the optimal outcome. My point is that given a high degree of Fed risk aversion, the Fed will not choose to follow model B, and this result will not depend on the severity of the consequences in model B of not following model B.

Thus, if your desired Fed rule requires strong commitment to work, you will not make your case any more persuasive by warning of ever more dire consequences if the Fed does not accept your model.

I don't think Taylor actually believes that his specific rule is the only good one, but he seems to have somehow gotten into his mind something like, "If the Fed were following any rule, obviously it would be mine, so when the Fed deviates from my rule, that is discretionary policy, which is bad."

If that's what he thinks, he has just a teency-weency bit of a point. For all we know, the Fed may actually be following a rule, and we just don't know what it is. The real problem (for rules advocates) is not that the Fed doesn't have a rule (which may or may not be the case) but that it hasn't announced its rule, which is definitely the case and which leads private agents to expect time-inconsistent behavior and therefore behave badly themselves. I think what Taylor is really saying is, "I gave you the clearest sunspot anyone could have given you, and yet you f___ers ignored it! If my wonderful paper can't get you to coordinate on a rule, then I don't know what can! Apparently there's no hope for you: you're among the damned, and I'm now going to shun you!"

And in the light of my last comment, I think Taylor actually has a better case then Beckworth. Taylor actually did publish a very widely cited paper that advocated a specific rule. I'd say, if there was any plausible sunspot, then the original Taylor rule was it. Beckworth doesn't really have a good sunspot candidate. Either he is saying, "My way or Hell!" or else he requires us to believe both (1) that NGDP targeting is the most plausible sunspot category and (2) that the specific sunspot implicit in the behavior of NGDP prior to 2002 would have been estimated the way he estimates it. The former is tenuous. The latter just seems silly: the pre-2002 trend depends entirely on what year you start your fit.

"I gave you the clearest sunspot anyone could have given you, and yet you f___ers ignored it! If my wonderful paper can't get you to coordinate on a rule, then I don't know what can! Apparently there's no hope for you: you're among the damned, and I'm now going to shun you!"

LULZ!

Anyway, my general intuition on "rules vs. discretion" has always been that there is just no way that the Fed is ever going to commit to a public rule. I can think of many reasons why this is true, and very few reasons to think it might ever happen. So I think we should be talking mostly about how to make discretion more rule-like, instead of what the perfect rule is. This post is just one reason why I have the intuition I do...

"Anyway, my general intuition on "rules vs. discretion" has always been that there is just no way that the Fed is ever going to commit to a public rule. I can think of many reasons why this is true, and very few reasons to think it might ever happen. So I think we should be talking mostly about how to make discretion more rule-like, instead of what the perfect rule is. This post is just one reason why I have the intuition I do..."

Noah, I think getting a rule done is actually pretty easy. But, before that I'd suggest you don't like the idea of brutal rule following by nature.

But I don't want to put words in your mouth.

Can you explain your best "many reasons why this is true" but when doing so imagine I'll be looking for underlying assumptions that promote your worldview.

Remember we want to observe without opinion before we form policy, right?

Off subject, I just realized that even if Christians or Muslims are screwed in the two-sided Pascal's Wager, if there's a third choice, namely atheism, then atheism is a worse choice than either of the others, since there is no opportunity of infinite rewards and a non-zero opportunity of infinite punishment.

Let me just add that even if the choice is between two incompatible models, I'm not sure that one can treat them as a wager since one of them could be right and, if it is, then the other one is wrong. And unlike the choice of religions, one could try to evaluate each of them empirically.

In case anybody's interested, I made a short criticism of Mr. Taylor's most recent blog post on my own blog, http://socialmacro.blogspot.com/2012/04/john-taylor-and-great-recession.html

Taylor criticized NGDP targeting because he thinks it is in fact discretionary:"Like the wolf dressed up as a sheep, it is discretion in rules clothing."http://johnbtaylorsblog.blogspot.jp/2011/11/more-on-nominal-gdp-targeting.html

So, in the eyes of Taylor, it's not rule vs rule (Christianity vs Islam) problem. It's still rule vs discretionary (Christianity vs atheist) problem. To borrow the concept of "The Last Battle" in The Chronicles of Narnia, it's not Aslan vs Tash problem, but Aslan vs Tashlan problem.

The fact is that Taylor has changed his mind a couple of times about this (there is ah, i think an early nineties or late eighties paper where he argued in favor of an ngdp target. have to look it up).

But lets be honest, if a rule was named after me i would be its biggest proponent too. My rule RULES!

A) Yes, he does. Ex. http://johnbtaylorsblog.blogspot.jp/2011/05/new-study-questions-justification-for.htmlBut he specifically criticized NGDP targeting for its lack of instrument rules. That criticism surely doesn't apply to the variants of Taylor rules which he abhors.